Add 1 teaspoon of lemon juice to the lobster essence and bring to a simmer in a small noncorrosive saucepan. Reduce the heat to low and whisk in 8 ounces of butter, 1 ounce at a time. Do not let the sauce boil. Season with salt and pepper. Hold over warm water or in a warm place.
Blanch the herb leaves in boiling water for 30 seconds. Drain, rinse under cold water, and squeeze dry. Chop the herbs very fine and combine them with the egg yolks and the remaining teaspoon of lemon juice in a stainless-steel bowl. Set the bowl over a pot of simmering water and whisk constantly until the mixture starts to thicken. Do not let the egg curdle. Whisk in 8 ounces of butter, 1 ounce at a time. If the sauce becomes too thick, thin it with a few drops of warm stock or water. Season with salt and pepper and transfer it to a clean bowl. Cover the surface of the sauce with plastic wrap or a thin film of butter to prevent it from forming a skin. Hold over warm water.
Cook the potatoes in salted water until done, about 10 minutes. Drain and peel if you wish. Keep warm.
Stem the beans and have ready boiling salted water.
Put the fish stock, shallots, and 2 ounces of butter in a large sauté pan. The pan should be large enough to hold the fish in one layer. Lightly salt and pepper the fish fillets and put them in the stock skin side down. Bring the liquid to a low simmer. Cover the pan and cook until the fish is done, about 2 minutes. Remove the fish from the stock and drain. Reserve the stock.
While the fish is poaching, cook the beans until done, 3 to 4 minutes. Drain them well and toss in a bowl with 1 ounce of butter. Season. Cut the potatoes in half, toss in the remaining 1 ounce of butter, and season.
Have ready 4 warm plates. Sauce the plates with the lobster sauce first. Place the fish on top and surround with the vegetables. Spoon the hollandaise on top of the fish and serve.